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Maths is a journey and long-term goal, achieved through exploration, clarification, practice and application over time. At each stage of learning, children should be able to demonstrate a deep, conceptual understanding of the topic and be able to build on this over time. 

Our overall aims for when children leave St. John’s Nursery and Infants and Fair Field Junior School are:

  • we ensure children feel confident to apply their skills to everyday life and understand that maths is all around us and intrinsic to a successful life.
  •  develop a positive attitude to mathematics as a subject in which all children gain success and pleasure.
  •  have access to a high quality maths curriculum that is both challenging and enjoyable, and builds upon previous learning.
  • be provided with a variety of mathematical opportunities, which will enable them to make relevant connections.
  • ensuring children are confident mathematicians who are not afraid to take risks.
  • children are confident when reasoning and make appropriate decisions, applying mathematical thinking in order to solve problems.
  • develop an ability to express themselves fluently, to talk about the subject with assurance, using correct mathematical language and vocabulary. 
  • develop mathematical skills and knowledge and recall of basic number facts and the four operations 
  • be able to use this knowledge and understanding to carry out calculations mentally
  •  make use of pictorial representations and informal notes to help record steps and part answers when using mental methods that generate more information than can be kept in their heads 
  •  have an efficient, reliable, compact written method of calculation for each operation that children can apply with confidence when undertaking calculations that they cannot carry out mentally. 

They will do this by always asking themselves: Can I do this in my head? Can I do this in my head using pictorial representations? Do I need to use a pencil and paper procedure of a formal written method?


The school uses Herts For Learning ‘ESSENTIAL Maths’ as the scheme of work that provides continuity and progression ensuring appropriate pitch and coverage of the curriculum. We continue to modify to match with our school’s approach and the needs of our pupils.

This policy is a statement of the aims, principles and strategies for teaching and learning of calculation strategies in Mathematics. It is designed to help teachers and staff at St. John’s Nursery and Infant School and Fair Field Junior School ensure that calculation is taught consistently across the school and to aid them in helping children who may need extra support or challenges. This policy is also designed to help parents, carers and other family members support children’s learning by providing an explanation of the methods used in our school.

The policy is set out according to the 4 operations, addition, subtraction, multiplication and division; and incorporates fractions for KS2. Within each specific area there is a progression of skills, knowledge and layout for written methods. The calculation strategies which will be used will reflect this ideology – moving from concrete to pictorial and then abstract recording leading to more formal written methods. The expectations are that teachers follow this to ensure consistency in approach and delivery at the appropriate stage. Mental methods and strategies will work in partnership with these methods. A variety of mental calculation methods will be taught and that recall of facts will be taught in school and tested regularly. The progression of mental methods and expectations will comply with the National Curriculum Statements 2014. It is important staff throughout the trust use the correct mathematical language and encourage pupils to do this also, which will help them develop confidence in their mathematical processes and reasoning. This will take place in class discussions as well as through oral and written feedback, next steps and target setting. The basis of our maths calculation policy is that written methods are complementary to mental methods and should not be seen as separate from them.

The Importance of Mental Mathematics 

While this policy focuses on written calculation in mathematics, we recognise the importance of mental strategies and known facts that form the basis of all calculations. Pupils are provided with frequent opportunities to compare and evaluate different calculation strategies. This helps them develop an understanding that efficiency is personal and based on the numbers involved. Mental maths fluency underpins all effective written calculation approaches. 

Concrete, Pictorial and Abstract 

Concrete - Manipulatives are objects that can be touched and moved by pupils to introduce, explore or reinforce a mathematical concept. They provide a vehicle to help pupils make sense of complex, symbolic and abstract ideas through exploration and manipulation. Furthermore, they support the development of internal models and help build stronger memory pathways. All pupils should have frequent opportunities to develop their understanding of mathematical concepts through the appropriate use of concrete apparatus. 

Concrete resources that may be found in classrooms will include: 

These resources will vary depending on year group and individual needs. At home, pupils very well may not have access to these school resources; however, they are just a vehicle to support a pupil’s understanding of a topic. Any objects can be used at home to replace counters, cubes etc. 

Pictorial (including jottings)  - The act of translating the concrete experience into a pictorial representation helps focus attention on what has happened and why. This supports deeper understanding and a stronger imprint on memory. Pictorial representations are more malleable than concrete resources and, once understanding is secured, allow exploration of complex problems that may be challenging to reproduce with manipulatives. When a child is working at the pictorial stage, it often provides rich opportunities for assessment of their depth of understanding.

Abstract - Written The aim, within this policy, is for compacted forms of notation. These have developed through the history of mathematics. Explicit individual steps in procedure are hidden or they have been shortcut. The informal and expanded methods expose all the intermediate steps, replicating thought processes more closely and support understanding prior to compaction. 

Abstract - Spoken Learning to use the correct mathematical vocabulary is vital for the development of mathematical proficiency. The ability to articulate accurately allows pupils to communicate and build meaning. Ideas become more permanent. This can be scaffolded effectively using speaking frames.


Pupils will leave us prepared for the next stage in their lives with: 

  • Pupils have an appreciation for the maths in everyday life
  •  Quick recall of facts and procedures 
  • The flexibility and fluidity to move between different contexts and representations of mathematics 
  • The ability to recognise relationships and make connections in mathematics 
  • Confidence and belief that they can achieve 
  • The knowledge that maths underpins most of our daily lives 
  • Skills and concepts that have been mastered 
  • Have a positive and inquisitive attitude to mathematics as an interesting and attractive subject in which all children gain success and pleasure. 

A mathematical concept or skill has been mastered when a child can show it in multiple ways, using the mathematical language to explain their ideas, and can independently apply the concept to new problems in unfamiliar situations and this is the goal for our children. These will be assessed through: assessment, tracking, pupil progress meetings, performance management, moderation and standardisation.

Fair Field Junior School

Watford Road, Radlett, Hertfordshire, WD78LU

Tel: 01923856341